My research has focused on developing free energy calculation methods that use available computer time more efficiently. I have been primarily interested in methods that quickly estimate free energies for many compounds based on few simulations. This will make it possible to, among other things, estimate the binding free energies of many ligands to a given receptor without the computational expense of doing a traditional free energy perturbation (FEP) calculation for each. After promising ligands are identified, traditional FEP calculations can be done to determine their binding free energy more accurately. The best ligand can be used as a new lead and the above procedure repeated. The method is based on traditional FEP methods but stores coordinates during simulations of reference compounds for use after the simulation is complete. In the first test of this method, we simulated seven small solutes in a box of water to determine solvation free energies. The seven solutes were: nothing, methane, ethane, propane, X1, X2, and X3 (where X1 is an ``atom'' that is somewhat smaller than carbon, X2 is a dimer, and X3 is a trimer). The coordinates from the seven different simulations were combined and the resulting set of coordinates was considered to have come from a simulation. Standard FEP methods are used to find the solvation free energy for solutes relative to this composite state. The relative solvation free energies for nothing, methane, ethane, and propane are all within less than 0.1 kcal/mol of the previously calculated values. This good agreement is not surprising considering a simulation was done for each of these solutes. The solvation free energies for additional solutes that were not simulated were in reasonable agreement with previous results. For example, methanol's calculated solvation free energy is underestimated by about 1 kcal/mol, where the previous result was 7 kcal/mol. Although quantitatively disappointing, this is impressive qualitatively because the calculation shows much of the expected hydrogen bonding between methanol and water even though it is based on simulations of only hydrophobic solutes. In general, we feel that our results indicate that the method gives reasonable estimates of solvation free energies and can be useful for predicting qualitative free energy differences. We are currently performing simulations of a beta-lactamase bound to a known inhibitor, clavulanate. This enzyme hydrolyzes beta-lactam antibiotics, giving bacteria antibiotic resistance, so drugs that inhibit them would be clinically useful. We intend to use the method described above to try to find improved inhibitors of beta-lactamase, possibly leading to new drugs.